The maximum number of halving lines and the rectilinear crossing number of Kn for n ≤ 27

For n ≤ 27 we present exact values for the maximum number h (n) of halving lines and over(h, ̃) (n) of halving pseudolines, determined by n points in the plane. For this range of values of n we also present exact values of the rectilinear over(c r, -) (Kn) and the pseudolinear over(c r, ̃) (Kn) crossing numbers of the complete graph Kn. over(h, ̃) (n) and over(c r, ̃) (Kn) are new for n ∈ {14, 16, 18, 20, 22, 23, 24, 25, 26, 27}, h (n) is new for n ∈ {16, 18, 20, 22, 23, 24, 25, 26, 27}, and over(c r, -) (Kn) is new for n ∈ {20, 22, 23, 24, 25, 26, 27}. © 2008 Elsevier B.V. All rights reserved.

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